Thermo Notes
Thermo Notes
1. What will be the resulting pressure if the air is three pound at 25psi and 15O° C is
   heated at constant volume of 30O0 F .
Solution:
                                      p1 p2
                                        =
                                      T1 T2
                             25psi            v2
                                       =
                          15O0 C + 460K 30O0 F + 460K
Final Answer:
P2 = 31.15psi
2. A 3.3 liters of an ideal gas is contained at 6.6atm and 25°C. How many moles of
   this gas are present?
Solution:
                                             PV       nRT
                        PV = nRT                  =
                                             RT       RT
                        T = °𝐶 + 273K
                        T = 250 C + 273K
                                                      PV
                        T = 298K               𝑛=
                                                      RT
Final Answer:
                              N= 0.890mol
3. A hot air balloon has a constant pressure of 600kPa and 250°𝐶. How many
   moles of air must be put into the balloon for 250KJ of work to be done on the
   balloon?
Solution:
                               PV       nRT
                                    =
                               RT        RT
                                        𝑃𝑉            𝑊
                                𝑛 = 𝑅𝑇 𝑜𝑟 𝑛 = 𝑅𝑇
                               T = °𝐶 + 273𝐾
                               T = 250°𝐶 + 273K
                                T = 523K
Final Answer:
n = 0.057mol
                                        3 𝑎𝑡𝑚 (10𝐿)
   P2 = 2atm1                  V2 =        2 𝑎𝑡𝑚
   V2 =?
5. A sample gas at a temperature of 20°C occupies a volume of 5 liters and as
   a pressure of 2 atmospheres. Wat will be the new pressure of if the volume
   is reducing to 2 liters while keeping the temperature constant?
                                           2 𝑎𝑡𝑚 (5𝐿)
                  V2 = 2L           V2 =
                                              2 𝑎𝑡𝑚
P2 =?
Solution:
                  T1 = 25°C         T1 = 298.15K
                                    K°C
                  T2 = 50°C         T2 = 50°C + 273.15
                  P2 =?             T2 = 323.15K
                                    K°C
   P1     P
        = T2                  Final answer:
   T1         2
          𝑃 1 𝑇2
   P2 =                                            P2 = 1.08atm
            𝑇1
          1𝑎𝑡𝑚 (323.15𝐾)
   P2 =
                   298.15𝐾
7. A sample of gas has a pressure of 3 atmosphere and occupies a volume of 2
   liters at a temperature of 25°C. If the temperature is increased to 100°C while
   keeping the volume constant, what will be the new pressure?
Solution:
               P1 = 3atm          T1 = 25 + 273.15
               T1 = 25°C          T1 = 298.15K
                                  K°C
               T2 = 100°C         T2 = 100°C + 273.15
               P2 =?               T2 = 373.15K
                                   K°C
   𝑃1     𝑃
        = 𝑇2                      Final answer:
   𝑇1      2
          𝑃1𝑇2
   P2 =       𝑇1                          P2 = 3.75atm
          3 𝑎𝑡𝑚 (373.15𝐾)
   P2 =            298.15𝐾
Given:
               P1 = 20 psia                          m = 10 lb
               P2 = 120 psia                         R = 40 ft-lb/lb °f
                                                                 𝐵𝑡𝑢
               T1 = 40 + 460 = 500 °R                Cf = 0.25 𝑙𝑏− °R
                𝑝2          𝑛−1       𝑡2                    𝑏𝑡𝑢
            [           ]         =            𝐶𝑣 = 0.1986 𝑙𝑏−𝑟
                𝑝1          𝑛         𝑡1
RER’D:                                                    m = 65g
                                                                  𝑐𝑚
     A = mass at standard condition                       d = 32 𝑠 2
B = mass in Kg REQ’D:
SOLUTION:                                        SOLUTION:
                    𝐹𝑔𝐾                                                1𝑘𝑔
     (A)    m=                                            65𝑔 ×              =         0.065kg
                     𝑔                                               1000𝑔
                                                             𝑐𝑚         1𝑚                  𝑚
                (8818.4𝑙𝑏𝑓)(32.174
                                     𝑙𝑏𝑚 𝑓𝑡
                                        ∗ )               32 𝑠 2 ×             =       0.32𝑠 2
                                     𝑙𝑏𝑓 𝑠2                            100𝑐𝑚
           m=                   𝑓𝑡
                          32.174 2
                                𝑠                                                             𝑚
                                                                                       0.32
                                                                                   𝑚          𝑠2
                        m = 8818.4lbm            F = ma= (0.065kg)( 0.32𝑠 2)
                                                                                              𝑚
                                                                                       0.32
     (B)    8818.4lbm × 2.2046𝑙𝑏𝑚
                                     1𝑘𝑔
                                                   F = 0.021 N                                𝑠2
m = 4000kg
                                     1𝑠𝑙𝑢𝑔
     (C)    8818.4lbm × 82.174𝑙𝑏𝑚
                 m = 274.0847 slug
  3. The mass of a given airplane at       SOLUTION:
     sea level (g= 32.1 fps²) is 12                                        2000 𝑙𝑏𝑚
     tons. Find its mass in pounds,           (A) m = 12 tons ×              1 𝑡𝑜𝑛𝑠
     slugs, and kg and its gravitational
     weight in pounds when it's
     travelling at a 40 000ft elevation.                    m = 24 000lbm
     The acceleration of gravity                                   𝑚
     decreases by 3.33x10 raise to                          0.32                   1 𝑠𝑙𝑢𝑔
                                                            𝑠2 ×
                                              (B) m = 24 000lbm                  32.174 𝑙𝑏𝑚
     negative 6 for each foot of
                                                                   𝑚
     elevation.                                             0.32
                                                            m = 745.94 slugs
                                                                 𝑠2
GIVEN:                                                             𝑚
                                                            0.32      2            1𝑘𝑔
                                                            𝑠
                                              (C) m = 24 000lbm ×
     m = 12 tons                                                                 2.205 𝑙𝑏𝑚
                                                                   𝑚
     g = 32.1 fps   2                                       0.32  2
                                                            m = 𝑠10884.35kg
REQ’D:                                                             𝑚
                                                            0.32
                                                                   𝑠2
     A = MASS IN POUNDS
                                                            𝑚 – (3.33 × 10 )(h)
                                                                          -6
                                              (D) g40000 = gs∙L
     B = MAS IN SLUGS                                       0.32
                                                                   𝑠2            𝑓𝑝𝑠 2
                                           = 32.9 fps2 – (3.33 × 10-6                    ) (40 000ft)
                                                                                  𝑓𝑡
     C = MASS IN KILOGRAM
                                           g40 000 = 31.9668 fps2
     D = GRAVITATIONAL WEIGHT
IN POUNDS                                       𝑚𝑔       (745.94 𝑠𝑙𝑢𝑔)(31.9335 𝑓𝑝𝑠 2 )
                                           w=        =                 𝑠𝑙𝑢𝑔−𝑓𝑡
                                                𝑘                  1
                                                                       𝑙𝑏𝑓− 𝑠2
                                                          w = 23 320.47 lbf
                                                                 𝑚
                                                          0.32
                                                                 𝑠2
                                                                 𝑚
                                                          0.32
                                                                 𝑠2
4. What is the mass in grams and               SOLUTION:
   the weight in dynes and in gram-                         1𝑙𝑏𝑚             1𝑘𝑔           1000𝑔
   force of 18oz salt? local g is 9.65   (A) m = 18𝑜𝑧 ×                ×               ×
                                                             16𝑜𝑧          2.205𝑙𝑏𝑚         1𝑘𝑔
   m/s² and 1lbm = 16 oz.
                                                          m = 510.20 𝑔
   GIVEN:                                                        𝑚
        m = 18oz                                          0.32
                                                                 𝑠2               𝑚    100𝑐𝑚
                𝑚                                     𝑚𝑔      (510.20𝑔)(9.65 2 )(            )
        g = 9.65𝑠 2                         (B) w =        = 𝑚                𝑔∙𝑐𝑚
                                                                                  𝑠     1𝑚
                                                      𝑘   0.32             1
                                                                             𝑑𝑦𝑛𝑒∙𝑠2
          1lbm = 16oz                                            𝑠2
        h = 15ft
                                                                            t = 83min
  3. Air enters steadily at 5.21 kg/m³
     and 35 m/s. What is the mass
                                           SOLUTION:
     flow rate through the nozzle if the
     inlet area of the nozzle is 85 cm²?   ṁ = pAv
GIVEN:                                              𝑘𝑔
                                           = (5.21𝑚3 ) ( 85𝑐𝑚2 ) (100𝑐𝑚 )2 (35 𝑠 )
                                                                                  1𝑚                  𝑚
                 𝑘𝑔
     P = 5.21𝑚3                                     𝑘𝑔                            1𝑚 2             𝑚
           𝑚                               = (5.21𝑚3 ) ( 85𝑐𝑚2 ) (100𝑐𝑚 ) (35 𝑠 )
     v = 35 𝑠
     A = 85𝑐𝑚2                             FINAL ANSWER:
REQ’D:                                                                  𝑘𝑔
                                                     ṁ = 1.55
     (A) = MASS FLOW RATE                                                𝑠
                                           SOLUTION:
                                              (A)
  4. Two gaseous streams enter a                                𝑙𝑏             1 𝑓𝑡
                                           ṁ = P2 A2 V2 = (0.10𝑓𝑡 3 ) (60in²) (12 𝑖𝑛)2 v2
     combining tube and leave as a
                                           v2 = P2 A2 ṁ2
     single mixture. These data apply
                                                     𝑙𝑏                        1𝑓𝑡 2               𝑙𝑏
     at the entrance section:              = (0.10𝑓𝑡 3 ) (60in²)(144 𝑖𝑛2 )(16.67 𝑠 )
                                                                1𝑓𝑡
  B.) the flow and area at exit section.          (70𝑖𝑛 2 )(        )(400     𝑓𝑝𝑠)
                                                               12𝑖𝑛
                                              =                   𝑓𝑡3
                                                               12
  GIVEN:                                                          𝑙𝑏𝑚
                                                                  𝑙𝑏
     A1 = 70 𝑖𝑛2                              ṁ1 = 16.20 𝑠
     V1 = 400 fps                                                 𝑙𝑏                   𝑙𝑏
                𝑓𝑡 3                          ṁ3 = 16.20 𝑠 + 16.67 𝑠
     v1 = 12𝑙𝑏𝑚
     A2 = 60𝑖𝑛2                                                    𝑙𝑏
                       𝒍𝒃𝒎
                                               ṁ3 = 32.87 𝑠
     ṁ 2 = 16.67         𝒔
                   𝒍𝒃𝒎                                          𝐴3𝑉3                   𝑙𝑏      𝐴3 (300𝑓𝑝𝑠)
     P2 = 0.10 𝒇𝒕𝟑                                  ṁ3 =                = 32.87 𝑠 =                𝑓𝑡3
                                                                 𝑣3                               6
                                                                                                    𝑙𝑏
     V3 = 300fps
           𝑓𝑡 3
     v3 = 6𝑙𝑏𝑚                                          32.87           50𝐴3
                                                    =            =                          A3 = 0.6574ft2
                                                          50             50
                             CONSERVATION OF ENERGY
   1.) A reversible non-flow constant volume process decreases the internal energy by
    316.5 kJ for 2268 kg of a gas for which =430 J/ kg-k and k = 1.35 For the process,
    determine: (a) Non-flow Work, (b) Heat, (c) All, (d) AH, and (e) The change of
    entropy if the initial temperature is 204.4°C
Solution:
                                                                                                363.812
    c.) Δ𝑢                                                        = 2.268 × 1.122857) 𝐼𝑛 (                )
                                                                                                 477.4
                 𝑟        430
          𝑐𝑣 = 𝑘−1 =    1.35−1
        Δ𝑢 – mcv ( T2 – T1)
      = (2.268 × 1.22857) (369.81 − 477.4)
             Δ𝑢 = −361.5 𝑘𝑗
    2.) 8 lbs of air drops from 80 psia to 5 psig. For an internally isothermal reversible
        process at 88°F, determine: (a) non-flow work, (b) Steady flow work, (c) 0. (d)
        Alf and AH, and (e) AS.
Given:
          T = 88 + 460 = 540 °R
          m = 81 lb
          P1 = 80 psia
          P2 = 5 + 14.7 = 19.7 psia
Solution:
                                                                                      𝑄
             𝑤𝑛 = 421.2 𝐵𝑡𝑢                                             e.) Δ𝑆 =
                                                                                     𝑇
                                                                                 421.2
                                                                            =    548
          b.) Steady flow-work
                               𝑣2                                                         𝐵𝑡𝑢
              ∫ 𝑉𝑑𝑝 − 𝑝1 𝑣1 𝐼𝑛 𝑣1                                           = 0.7686 ( °R )
             = 421.1 𝐵𝑡𝑢
          c.) Q = Δ𝑣 + 𝑊𝑛
              = 421.2 𝐵𝑡𝑢
                                                                                                        𝐵𝑡𝑢
          3.) Steam enters turbine with an enthalpy of 1292                                                   and leaves an enthalpy of
                                                                                                         𝑙𝑏
                      𝐵𝑡𝑢                                                    𝐵𝑡𝑢                                    𝐵𝑡𝑢
               1098            , Transferred Heat is 13                            . What is the work in 𝑚𝑖𝑛 and hp per a flow
                       𝑙𝑏                                                    𝑙𝑏
                     𝑙𝑏
               of 2 𝑠𝑒𝑐?
                                           𝐵𝑡𝑢                                             𝐵𝑡𝑢
      Given:        h11       = 1292                                       h2 = 1098
                                               𝑙𝑏                                              𝑙𝑏
                                 𝐵𝑡𝑢                                                      𝑙𝑏
                    a = 13                                                 flow = 2 𝑠𝑒𝑐
                                     𝑙𝑏
Solution:
                    h1 – a = h2 + w
                    w = h1 – (h2+9)
                                          𝐵𝑡𝑢                        𝐵𝑡𝑢             𝐵𝑡𝑢
                    w = 1292                        – [ (1098              ) + 13          ]
                                        𝑙𝑏                            𝑙𝑏             𝑙𝑏
                                      𝐵𝑡𝑢            2𝑙𝑏       1 ℎ𝑝
                    w = 181                        x 𝑠𝑒𝑐 x          𝐵𝑡𝑢
                                          𝑙𝑏                 4.24
                                                                     𝑙𝑏
w= 512.264 hp
                                                                             𝐾𝑔
             4.)An air compressor receives 272 𝑚𝑖𝑛 . of air at 99.29 kPaa and a specific
                                                   m³
               volume of 0.026 𝑘𝑔 . The air flows steady the compressor and is discharged at
                                                              m³                                                                  𝐽
               689.5 kPaa and 0.0051 𝑘𝑔 . The initial internal energy of the air is 1594 𝑘𝑔 ; at
                                                                                      𝐽
               discharge, the internal energy is 6241 𝑘𝑔 . The compressor rejects heat at
                          𝐽
               4383 𝑘𝑔 . The change in kinetic energy is 896 J/kg increase. Compute the work
               in kW.
                                                                                           𝐾𝑔
      Given:        p1 = 99.29 kPa                                         m = 272 𝑚𝑖𝑛
                                              m³
                    v1 = 0.026 𝑘𝑔                                          p2 = 689.5 kPa
                                           𝐽                                                       m³
                    u1 = 1594 𝑘𝑔                                           v2 = 0.0051 𝑘𝑔
                                               𝐽                                               𝐽
                    Q = -4363 𝑘𝑔                                           u2 = 6241 𝑘𝑔
                                          𝐽
                    Δk = 896 𝑘𝑔
      Solution:
         w      ?     Q                                    = P1 + K1 + Wf1 + V1 + Q = P2 + K2 + Wf2 + U2 + W
 K1                             K2                            Basis 1Kgm
Wf1                             Wf2                                                                                 m³
                                                           Wf1 = P1 V1 = [99.29 KN/m2] [ 0.026                           ]
                                                                                                                    𝑘𝑔
 U1     energy diagram.         U2                                           𝐾𝐽
                                                                = 2583 𝑘𝑔
                                                           Wf2 = P2 V2 = [689.5 Kn/m2]
                                                                        𝐾𝐽
                                                               = 3.516 𝑘𝑔
                                                     Wf1 + V1 + Q = ΔK = Wf2 + V2 + W
                                           = 2.582 = 1. 594 – 4. 383 = 0.896 + 3.156 + 6.241 + W
                                                                           𝐾𝐽
                                                               W = -10.86 𝑘𝑔
                                                                                           𝐾𝐽                  𝑘𝑔
                                                                      W = [-10.86 𝑘𝑔 ] [ 272 𝑚𝑖𝑛 ]
                                                                                                        𝐾𝐽
                                                                                  W= -2954 𝑚𝑖𝑛
5. A 50kg block is released from its resting position at a height of 10m from the
   ground. If we neglect air resistance, what is the block's total energy at a
   height of 4m from the ground.
   GIVEN:
      m = 50kg
      h = 10m
   SOLUTION:
     PE = mgh
                  𝑚
     = (50kg) (9.8𝑠 2) (10m)
      = 4900J
   FINAL ANSWER:
     PE = 4.9kJ
   GIVEN:
                  𝑁
      k = 500 𝑚
      x = 0.1m
   SOLUTION:
          1
     PE = 2k𝑥 2
              1       𝑁
      PE = 2 (500𝑚) (0.1m)2
   FINAL ANSWER:
      PE = 2.5kJ
   GIVEN:
      m = 500kg
            𝑚
      V1 = 4 𝑠
     h = 10m and F = 500J
   SOLUTION:                                            FINAL ANSWER:
     PE1 + KE1 = PE2 + KE2 + F
                                                                         𝑚
PE1 + KE1 – F = KE2                                            V2 = 12.2𝑠 2
             1               1
   Mgh + 2 𝑚𝑣12 – F = 2 𝑚𝑣22
                            2f
   V2 =      2 gh  V12 
                            m
             m             m     2(500 J )
     2(9.8     2
                 (15m)  (9 )2 
             s             s      500kg
                                    DENSITY
1. A reservoir of glycerin has a mass of 1,200 kg and a volume of 0.952 cm³ Find
   the density.
   GIVEN:
        m = 112g
        v = 9.98cm3                   FINAL ANSWER:
   SOLUTION:
            𝑚                                            𝑔
        𝜌= 𝑣                                    𝜌 = 11.2 𝑚3
               112𝑔
          = 9.98𝑚3
3. A certain gas occupies a volume of 0.28 m³ and has a mass of 0.40 kg. What is
   the density of the gas?
   GIVEN: m = 0.40kg
        v = 0.28m3                    FINAL ANSWER:
   SOLUTION:
            𝑚                                                  𝑘𝑔
        𝜌= 𝑣                                        𝜌 = 1.42 𝑚3
              0.40𝑘𝑔
          = 0.28𝑚3
4. A certain gas fills a 3 Liter balloon and has a mass of 0.1 kg. What is the density
   of the gas?
   GIVEN:
        m = 0.1kg                     FINAL ANSWER:
        v = 3L
                                                               𝑘𝑔
   SOLUTION:                                       𝜌 = 0.033 𝐿
            𝑚
        𝜌= 𝑣
              0.1𝑘𝑔
          =    3𝐿
                                              TEMPERATURE
1. Define a new temperature scale, say "N, in which the boiling and freezing point are
       1000°N and 100°N, respectively, and correlate this scale with the Fahrenheit and
       Celsius scales. What is the absolute temperature at "N?
By interpolation:
100                         900 °c
                 =
°c                         −100°N
−1000                      900 °c
                 =
 900                        900
n= -11.11 °c
SOLUTION:
                 5
          °C =       ( F- 32 )                       °R = F + 460
                 9
                 5
             =       ( 400 – 32 )                      = 400 + 460
                 9
            = 204.44 °C                                = 860 °R
         °K = c + 273
            = 204.44 °C + 273
            = 477.44 °K