Question

An expandable cube, initially 20 cm on each side, contains 3.0 g of helium at 20°C. 1000 J of heat energy are transferred to this gas. What are (a) the final pressure if the process is at constant volume and (b) the final volume if the process is at constant pressure?

Answer 1

a) The final pressure is approximately 3.4 atm. b) The final volume is approximately 33 L. These calculations elucidate the final pressure and volume within the specified conditions of the gas system.

Step-by-step explanation:

(a) The determination of the final pressure involves utilizing the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

With a constant volume, the equation is rearranged as P = (nRT)/V.

Substituting the provided values, P = (3.0 g / (4 g/mol)) * (0.0821 L.atm/(mol.K)) * (293 K) / (20 cm), yielding a final pressure of approximately 3.4 atm.

(b) For the final volume, the ideal gas law equation is once again applied, PV = nRT.

Since the process occurs at constant pressure, the equation is rearranged as V = (nRT)/P.

Substituting the values, V = (3.0 g / (4 g/mol)) * (0.0821 L.atm/(mol.K)) * (293 K) / (3.4 atm), resulting in a final volume of approximately 33 L.

These calculations elucidate the final pressure and volume within the specified conditions of the gas system.

Answer 2

The total change in internal energy of the gas is 117 J.

Step-by-step explanation:

In order to solve this problem, we need to use the first law of thermodynamics which states that the change in internal energy of a system equals the heat added minus the work done by the system. Since the process is at constant volume, no work is done, so the change in internal energy is equal to the heat added. Therefore, the total change in internal energy of the gas is 117 J.