Question

what is the value of w (work) when 2.6 moles of h2 expands from 25 liters to 50 liters against a constant external pressure of 1 atm, then expands further from 50 to 100 liters against a constant external pressure of 0.1 atm? answer in calories. answer in units of cal.

Answer 1

The work done by the gas during both expansions is -726.14 calories.

Step-by-step explanation:

To calculate the work done (w) when a gas expands, we use the formula w = -Pext ΔV where Pext is the external pressure and ΔV is the volume change. We need to consider each expansion separately since they occur under different external pressures.

For the first expansion from 25 liters to 50 liters at 1 atm:

• ΔV = 50 L - 25 L = 25 L
• w = -1 atm × 25 L = -25 L·atm

For the second expansion from 50 liters to 100 liters at 0.1 atm:

• ΔV = 100 L - 50 L = 50 L
• w = -0.1 atm × 50 L = -5 L·atm

To convert L·atm to calories, we use the conversion 1 L·atm = 101.3 J and 1 J = 0.239005736 cal.

w (total) = w (first expansion) + w (second expansion)

w (total) = -25 L·atm - 5 L·atm = -30 L·atm

Now convert L·atm to J: w (total) = -30 L·atm × 101.3 J/L·atm = -3039 J

Convert J to cal: w (total) = -3039 J × 0.239005736 cal/J = -726.14 cal

The value of work done by the gas is -726.14 calories.