Question

An expandable cube, initially 20 cm on each side contains 2.7 g of helium at 20 C. 1200 J of heat energy are transferred to this gas. What are (a) the final pressure if the process is at constant volume (in atm) and (b) the final volume if the process is at constant pressure (in cm^3)?

Answer 1

To solve for the final pressure and final volume of the helium gas, we can use the ideal gas law. If the process is at constant volume, we can use the formula PV = nRT to find the final pressure. If the process is at constant pressure, we can use the formula V = (nRT)/P to find the final volume.

Step-by-step explanation:

In this problem, we are given an expandable cube that contains helium at a certain temperature and initial volume. From the information provided, we can solve for the final pressure and final volume of the gas, based on the conditions given.

(a) Final Pressure:

If the process is at constant volume, the volume remains the same. We can use the ideal gas law, PV = nRT, to solve for the final pressure.

We can rearrange the formula to solve for pressure:

P = (nRT)/V

Given that the initial temperature is 20 °C and the gas constant R is 0.0821 L·atm/(mol·K), we can convert the initial temperature to Kelvin by adding 273.15: T = 20 °C + 273.15 = 293.15 K.

Substituting the values into the formula, we get:

P = (2.7 g/(4 g/mol))(0.0821 L·atm/(mol·K))(293.15 K)/(20 cm³)

Calculating the expression gives us the final pressure, in atmospheres.

(b) Final Volume:

If the process is at constant pressure, the pressure remains the same. We can use the ideal gas law to solve for the final volume.

Rearranging the formula gives us:

V = (nRT)/P

Substituting the values into the formula, we can solve for the final volume in cm³.