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1.) Suppose 157 moles of a monatomic ideal gas undergoes an isothermal expansion

ID: 2241586 • Letter: 1

Question

1.) Suppose 157 moles of a monatomic ideal gas undergoes an isothermal expansion as shown in the figure. (The horizontal axis is marked in increments of 4 m3.) How much work is done by the gas during this expansion?

https://general.physics.rutgers.edu/gifs/CJ/15-5.gif


2.) Nine moles of an ideal monatomic gas expand isothermally at a temperature of 51

Suppose 157 moles of a monatomic ideal gas undergoes an isothermal expansion as shown in the figure. (The horizontal axis is marked in increments of 4 m3.) How much work is done by the gas during this expansion? Nine moles of an ideal monatomic gas expand isothermally at a temperature of 51 degree C. If the volume of the gas quadruples during this process, what is the heat flow into the gas? Three moles of a monatomic ideal gas are heated at a constant volume of 2.10 m3. The amount of heat added is 5.44 times 103 J. Determine the change in pressure.

Explanation / Answer

1) work done by the gas = nR ln(Vf/Vi)


= 157 * 8.314 * ln(16/4)


= 157 * 8.314 * ln(4)


= 1809.527 J


= 1.80 KJ

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2)PV = n RT

T = constant = isothermal
V2 = 4 V1
dU = change in internal energy = function of temperature alone = 0 for isothermal

work done dW = [limit from V1 to V2] ? P dV = [limit from V1 to V2] ? nRT ? nRT [dV/V]
work done dW = n R T [Ln V] = n RT [ln {V2/V1}]
work done dW = n RT [ln 4] = 9 * 8.314 * [273+51] Ln 4 = 24243.624J = 33.60 KJ
======================================...
dQ = heat in = dU + dW = 33.60 KJ

heat flow into the gas = 33.60 KJ



3)?U = Q + W

Because volume does not change, no work is done on gas:
W = - ? p dV = 0
Hence:
?U = Q
The change of internal energy of an ideal gas is:
?U = n