A student is set this problem: of helium (a monatomic ideal gas with constant heat…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics

Thermal Physics, Ch The first law: work, heat and internal energy

Problem

A student is set this problem:

0.500\,\mathrm{mol}

of helium (a monatomic ideal gas with constant heat capacities) is held in a cylinder closed by a frictionless piston of negligible mass, with the outside pressure held at a constant

1.00\times10^{5}\,\mathrm{Pa}

. The gas is warmed slowly and quasistatically from

300\,\mathrm{K}

400\,\mathrm{K}

. How much heat is delivered to the gas? They write: "For an ideal gas

U

depends on

T

alone, so

(\partial U/\partial T)_p = (\partial U/\partial T)_V = C_V = \tfrac32 Nk_B = 6.24\,\mathrm{J\,K^{-1}}

. Therefore the heat delivered is

Q = C_V\,\Delta T = 6.24\times 100 = 624\,\mathrm{J}

." The book's convention is

\Delta U = Q + W

with

W

the work done on the gas. ((a)) Their first sentence is true, but the conclusion is wrong. Say exactly which step fails, and which held-fixed variable belongs on the heat capacity that answers this question. ((b)) Find the correct heat delivered, and the work done on the gas.

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