First slide

First law of thermodynamics

Question

In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas molecules give out 30 J of heat and 10 J of work is done on the gas. If the internal energy of the gas was 40 J, then the internal energy wiII be

Moderate

A

-20 J
B

20 J
C

80 J
D

30 J

Solution

Here dQ = d + dW
$\begin{array}{l} dU = U_{f} - U_{i} \\ ∴ dQ = (U_{f} - U_{i}) + dW \end{array}$
or $\begin{array}{l} U_{f} = dQ + U_{i} - dW \\ dQ = - 30 J \end{array}$
(heat is rejected by system)
$\begin{aligned} U_{i} = 40 J and dW = - 10 J \\ ∴ U_{f} = - 30 + 40 + 10 = 20 J \end{aligned}$

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