Question

A 2500 cm

3
container holds 0.13 mol of helium gas at 330
∘
C. How much work must be done to compress the gas to 1500 cm
3
at constant pressure? Express your answer with the appropriate units. How much work must be done to compress the gas to 1500 cm
3
at constant temperature? Express your answer with the appropriate units.

Answer 1

To compress the gas to 1500 cm3 at constant pressure, calculate the work using the formula: Work = Pressure * Change in Volume. To compress the gas to 1500 cm3 at constant temperature, calculate the work using the formula: Work = -Change in Internal Energy.

Step-by-step explanation:

To find the work done to compress the gas to 1500 cm3 at constant pressure, we can use the formula:

Work = Pressure * Change in Volume

Since the pressure is constant, the work done can be calculated as:

Work = Pressure * (Final Volume - Initial Volume)

Plug in the values:

Work = (0.13 mol * R * 330 K) * (1500 cm3 - 2500 cm3)

where R is the ideal gas constant.

To find the work done to compress the gas to 1500 cm3 at constant temperature, we can use the formula:

Work = -Change in Internal Energy

Since the temperature is constant, the change in internal energy can be calculated as:

Change in Internal Energy = -n * R * T * ln(Vf/Vi)

Plug in the values:

Change in Internal Energy = -0.13 mol * R * 330 K * ln(1500 cm3/2500 cm3)