True or false on processes

Problem

State whether each statement is true or false, justifying your answer.

• (a) In an isothermal process of an ideal gas $\Delta U = 0$.
• (b) In an adiabatic process $Q = 0$ implies $\Delta T = 0$.
• (c) In an isochoric process the work is $L = 0$.
• (d) The specific heat at constant pressure is greater than that at constant volume.
• (e) Temperature is a form of energy.

Solution

(a) TRUE. For an ideal gas the internal energy depends only on temperature: $U = U(T)$. In an isothermal process $T$ does not change, so $\Delta U = 0$.

(b) FALSE. In an adiabatic process $Q = 0$, but the first law gives $\Delta U = -L$: if the gas does or receives work, its internal energy changes and so does the temperature. In general $\Delta T \neq 0$ (the gas cools when expanding, heats up when compressed).

(c) TRUE. At constant volume there is no displacement of the system boundary, so $L = \int p\,\dd V = 0$.

(d) TRUE. Mayer’s relation holds: $C_p = C_v + R > C_v$: at constant pressure part of the heat supplied is used to do expansion work, so more is needed for the same temperature rise.

(e) FALSE. Temperature measures the average kinetic energy of the molecules, but it is not itself a quantity of energy: it is an intensive quantity, whereas energy is extensive. Doubling the amount of gas does not double the temperature, but it does double the energy.

$\ev{V,\ F,\ V,\ V,\ F}$

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Topics: Thermodynamics Concepts: Thermodynamic processes · First law of thermodynamics