Question

# A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is :

A
25
B
52
C
45
D
1

Solution

## The correct option is A $$\dfrac{2}{5}$$The heat Q is converted into the internal energy and work. According to the first law of thermodynamics,$$Q = U + W$$$$nC_p\Delta T=nC_v\Delta T+W$$The dfraction of heat converted to work is given as $$\displaystyle\dfrac{W}{Q}=\dfrac{nC_p\Delta T-nC_v\Delta T}{nC_p\Delta T}=\dfrac{C_p-C_v}{C_p}=\dfrac{{\dfrac{5}{2}R}-{\dfrac{3}{2}R}}{\dfrac{5}{2}R}=\dfrac{2}{5}$$Physics

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