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Practice Test — Thermodynamics Math
Practice Test — Thermodynamics Math
Practice Test — 20 Questions
1. Convert 25°C to Fahrenheit.
2. Convert 451°F to Celsius.
3. $Q = mc\Delta T$. Find $Q$: $m = 3$ kg, $c = 4186$, $\Delta T = 20$.
4. $PV = nRT$. Find $P$: $n = 2$, $T = 400$ K, $V = 0.05$ m³.
5. Boyle's law: $P_1 = 3$ atm, $V_1 = 4$ L, $V_2 = 6$ L. Find $P_2$.
6. Charles's law: $V_1 = 10$ L at 300 K. $V_2$ at 450 K?
7. Carnot: $T_H = 700$ K, $T_C = 280$ K. Max $\eta$?
8. Engine: $Q_{in} = 4000$ J, $\eta = 30\%$. Work?
9. $\Delta U = Q - W$. $Q = 1000$, $W = 400$. $\Delta U$?
10. Adiabatic: $Q = 0$, $W = 200$. $\Delta U$?
11. $\Delta S = Q/T$. $Q = 600$ J, $T = 300$ K. $\Delta S$?
12. What is 0°C in Kelvin?
13. An engine runs between 1000 K and 400 K. Carnot $\eta$?
14. 5 kg water heated from 10°C to 50°C. $Q$? ($c = 4186$)
15. Isothermal process: what is $\Delta U$?
16. At which temp do °C and °F equal?
17. Gas at 1 atm, 10 L compressed to 2 L. New pressure?
18. Can Carnot $\eta$ ever reach 1 (100%)?
19. Engine exhausts 700 J from 1000 J input. Efficiency?
20. Does entropy of the universe increase or decrease in spontaneous processes?
Show Answer Key
1. 77°F
2. $(5/9)(451-32) \approx 232.8$°C
3. $251{,}160$ J
4. $P = 2(8.314)(400)/0.05 = 132{,}624$ Pa ≈ 133 kPa
5. 2 atm
6. 15 L
7. $1 - 280/700 = 60\%$
8. 1200 J
9. 600 J
10. $-200$ J
11. 2 J/K
12. 273.15 K
13. 60%
14. $5(4186)(40) = 837{,}200$ J
15. 0
16. $-40$°
17. 5 atm
18. No — requires $T_C = 0$ K, impossible.
19. 30%
20. Increase (always)