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  1. Problems
  2. /A student says: 'In an isothermal expansion of an ideal gas the temperature does not change, so no…
MediumPhysicsHigh School (11–12)Heat & Thermodynamics › Thermodynamic Processes and Specific Heats of GasesConceptualBoard Exam

A student says: 'In an isothermal expansion of an ideal gas the temperature does not change, so no…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A student says: 'In an isothermal expansion of an ideal gas the temperature does not change, so no heat flows.' Find the mistake and write the correct statement. How much heat does 0.50 mol0.50\ \text{mol}0.50 mol at 400 K400\ \text{K}400 K take in when its volume triples? (R=8.31 J mol−1K−1R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}R=8.31 J mol−1K−1)

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

J
Need a reminder? The key ideaShowHide

Isothermal: ΔU=0\Delta U = 0ΔU=0, Q=W=nRTln⁡V2V1Q = W = nRT\ln\dfrac{V_2}{V_1}Q=W=nRTlnV1​V2​​. Isobaric: W=p ΔV=nR ΔTW = p\,\Delta V = nR\,\Delta TW=pΔV=nRΔT, Q=nCp ΔTQ = nC_p\,\Delta TQ=nCp​ΔT. Isochoric: W=0W = 0W=0, Q=ΔU=nCv ΔTQ = \Delta U = nC_v\,\Delta TQ=ΔU=nCv​ΔT.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The mistake. A steady temperature means ΔU=0\Delta U = 0ΔU=0, not Q=0Q = 0Q=0. The gas does work as it expands, so heat must flow in to replace that energy: Q=WQ = WQ=W.

Step 2. Heat. Q=0.50 mol×8.31 J mol−1K−1×400 K×ln⁡3=1826 JQ = 0.50\ \text{mol} \times 8.31\ \text{J mol}^{-1}\text{K}^{-1} \times 400\ \text{K} \times \ln 3 = 1826\ \text{J}Q=0.50 mol×8.31 J mol−1K−1×400 K×ln3=1826 J.

Answer: In an isothermal expansion the heat taken in equals the work done; here 1826 J1826\ \text{J}1826 J.

Watch out. 'No temperature change' and 'no heat' are different ideas; the adiabatic process is the one with no heat.

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  1. Isothermal, isobaric and isochoric processesSpecific Heats of Gases and Thermodynamic Processes

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