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NEET
Exam
NEET
Subject
Physics
Chapter
Thermodynamics

NEET · Physics · Thermodynamics

Heat is supplied to a monoatomic ideal gas at a constant rate of...

Heat is supplied to a monoatomic ideal gas at a constant rate of 150 W150\text{ W}. If the gas expands isobarically, the rate at which the gas does work is :

Options

  1. A90 W90\text{ W}
  2. B150 W150\text{ W}
  3. C60 W60\text{ W}
  4. D375 W375\text{ W}

Correct answer

C. 60 W60\text{ W}

Step-by-step solution

For a monoatomic ideal gas undergoing an isobaric process, the molar heat capacity at constant pressure is Cp=52RC_p = \dfrac{5}{2}R.

The heat supplied is given by dQ=nCpdT=52nRdTdQ = nC_pdT = \dfrac{5}{2}nRdT.

The work done by the gas during expansion is dW=pdV=nRdTdW = pdV = nRdT.

Taking the ratio of work done to heat supplied:
dWdQ=nRdT52nRdT=25\dfrac{dW}{dQ} = \dfrac{nRdT}{\dfrac{5}{2}nRdT} = \dfrac{2}{5}

Differentiating with respect to time tt, we get the relationship between their rates:
dWdt=25dQdt\dfrac{dW}{dt} = \dfrac{2}{5} \dfrac{dQ}{dt}

Given that the rate of heat supplied is dQdt=150 W\dfrac{dQ}{dt} = 150\text{ W}:
dWdt=25×150 W=60 W\dfrac{dW}{dt} = \dfrac{2}{5} \times 150\text{ W} = 60\text{ W}

Answer: 60 W60\text{ W}
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