1) A mol of an ideal monoatomic gas is placed in a container with a massless fri

Question

1) A mol of an ideal monoatomic gas is placed in a container with a massless frictionless piston that keeps the pressure at 1 atmosphere. The gas is heated at a rate of 600 watt such that its temperature increases by 12 degree C. a. How much will the internal energy of the gas change? b. How much will the volume change? c. How long will it take for the temperature to raise the 12 degree C d. If the piston is now fixed in place how long will it take for the temperature to raise 12 degree C? Explain the difference.

Explanation / Answer

1)

a)

here , as change in temperature , del T = 12 C

increase in internal energy = 3nR*del T/2

increase in internal energy = 1.5 * 8.314 * 12

increase in internal energy = 149.7 J

the increase in internal energy is 149.7 J

b)

let change in volume is V

Q = U + P* V

2.5 * R * T = U + P*V

2.5 * 8.314 * 12 = 149.7 + 1.01 *10^5 * V

V = 9.873 *10^-4 m^3

the change in volume is 9.873 *10^-4 m^3

c)

Now, as energy = power *time

time = (149.7+ 1.01 *10^5*9.873 *10^-4)/600

time = 0.42 s

the time taken is 0.42 s

d)

For fixed pressure ,

heat = U

heat = 1.5 * 8.314 * 12

U = 149.7 J

Now, time taken is t = 149.7/600

t = 0.25 s

the time taken is 0.25 s

here , as the work done by the gas is zero

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