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Thermodynamics Quick Reference
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1
Question
State the first law of thermodynamics in energy form.
Answer
ΔQ = ΔU + W
2
Question
What is the work done in an isobaric process in terms of pressure and volume change?
Page 1
Answer
W = PΔV
3
Question
How is heat related to temperature change for an isobaric ideal gas with amount n?
Page 1
Answer
ΔQ = nC_pΔT (and W = nRΔT)
4
Question
What is the work done in an isochoric process?
Page 1
Answer
W = 0
5
Question
For an isochoric ideal gas, how does heat relate to internal energy change?
Page 1
Answer
ΔQ = ΔU = (f/2) nR ΔT
6
Question
Write the expression for work done during a reversible isothermal expansion of an ideal gas.
Page 1
Answer
W = nRT ln(V2/V1)
7
Question
Why is internal energy change zero for an ideal gas in an isothermal process?
Page 1
Answer
Because internal energy depends only on temperature, and ΔT=0
8
Question
State the relation between Cp and Cv for ideal gases.
Page 1
Answer
C_p - C_v = R
9
Question
Define a polytropic process and its general PV relation.
Page 1
Answer
A polytropic process follows PV^a = k (a is polytropic exponent)
10
Question
Express work for a polytropic process where PV^a=k.
Page 1
Answer
W = ∫P dV = (k/(1-a))(V_f^{1-a} - V_i^{1-a})
11
Question
How can the polytropic work expression be written using pressures and volumes?
Page 1
Answer
W = (P_f V_f - P_i V_i)/(1-a)
12
Question
What is the specific heat for a polytropic process in terms of Cv and a?
Page 1
Answer
C = C_v + R/(1-a)
13
Question
Give the efficiency formula of a heat engine in terms of Qin and Qout.
Page 3
Answer
Efficiency = W/Q_in = 1 - Q_out/Q_in
14
Question
For a Carnot engine, express efficiency using reservoir temperatures.
Page 4
Answer
Efficiency = 1 - T_sink/T_source
15
Question
How are heat transfers for Carnot isothermal legs expressed for an ideal gas?
Page 4
Answer
Q_in = nR T_1 ln(V_B/V_A); Q_out = nR T_2 ln(V_C/V_D)
16
Question
What condition yields 100% (unity) Carnot efficiency?
Page 4
Answer
T_sink = 0 K (absolute zero)
17
Question
What relation holds between heat ratios and temperature ratios for reversible Carnot processes?
Page 4
Answer
Q_1/Q_2 = T_1/T_2
18
Question
State the first-law energy balance for a refrigerator in terms of Q1, Q2, and W.
Page 5
Answer
Q_2 = Q_1 + W
19
Question
Define coefficient of performance (COP) β for a refrigerator.
Page 5
Answer
β = Q_1 / W = Q_1 /(Q_2 - Q_1)
20
Question
Express refrigerator COP in terms of temperatures for an ideal reversible refrigerator.
Page 5
Answer
β = T_inside /(T_high - T_inside)
21
Question
In a free (Joule) expansion of an ideal gas into vacuum, what is the work done and why?
Page 2
Answer
W = 0 because no external pressure does work during expansion into vacuum
22
Question
For free expansion of an ideal gas in an insulated container, what happens to internal energy and temperature?
Page 2
Answer
ΔU = 0 and ΔT = 0 for ideal gas (no heat/work exchange)
23
Question
State the adiabatic condition for a reversible adiabatic (isentropic) ideal gas.
Page 1
Answer
PV^γ = constant
24
Question
How is γ related to degrees of freedom f for an ideal gas?
Page 1
Answer
γ = 1 + 2/f (equivalently γ = C_p/C_v)
25
Question
Write the relation between initial and final states for pressure and volume in an adiabatic process.
Page 1
Answer
P_1 V_1^γ = P_2 V_2^γ
26
Question
Provide an expression for work done during an adiabatic process using state variables.
Page 1
Answer
W = (P_2 V_2 - P_1 V_1)/(1-γ) = nR ΔT /(1-γ)
27
Question
How do slopes dP/dV differ between isothermal and adiabatic processes on a PV diagram?
Page 1
Answer
dP/dV = -P/V (isothermal) vs -γP/V (adiabatic); adiabatic is steeper
28
Question
Explain why sudden piston movement tends to produce an adiabatic process.
Page 1
Answer
Rapid change prevents heat exchange with surroundings, so δQ≈0