Question

# One mole of an ideal monoatomic gas is heated at a constant pressure from $$0$$ to $$100$$. Then the change in the internal energy of the gas is:(Given, $$R=8.32J{ mol }^{ -1 }{ K }^{ -1 }$$)

A
0.83×103J
B
4.6×103J
C
2.08×103J
D
1.25×103J

Solution

## The correct option is C $$1.25\times { 10 }^{ 3 }J$$Given :        $$T_i = 0 ^oC = 273 K$$              $$T_f = 100 ^oC = 373 K$$            $$n = 1$$For monoatomic gas            $$C_v = \dfrac{3R}{2}$$$$\therefore$$   Change in internal energy of the gas          $$\Delta U = nC_v \Delta T$$   $$\Delta U = \dfrac{3R}{2}n (T_f - T_i) = 1\times \dfrac{3}{2} \times 8.314 \times (373-273)$$$$\implies$$   $$\Delta U = 1.25 \times 10^3$$  $$J$$Physics

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