Question

For an ideal gas

Easy

A

the change in internal energy in a constant pressure process from temperature $T_{1} to T_{2}$ is equal to ${nC}_{V} (T_{2} - T_{1})$ , where C, is the molar specific heat at constant volume and n the number of moles of the gas.
B

the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
C

the internal energy does not change in an isothermal process.
D

no heat is added or removed in an adiabatic process.

Solution

$(a) ΔV = {mC}_{V} ΔT = {nC}_{V} (T_{2} - T_{1}) (b) dQ = dU + dW$
but $dQ = 0 (adiabatic process)$
$∴ dU = - dW or | dU | = | dW |$
$(c) dU = {mC}_{V}, dT$
$(dT = 0, isothermal process)$
$∴ dU = 0$
$(d) dQ = 0 in adiabatic change .$
Hence all are correct.

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