Question

An ideal gas is kept in a cylinder of volume \(3 \, {m}^3\) at a pressure of \(3 \times 10^5 \, {Pa}\). The energy of the gas is

• A. \(13.5 \times 10^6 \, {J}\)
• B. \(1.35 \times 10^5 \, {J}\)
• C. \(13.5 \times 10^5 \, {J}\)
• D. \(135 \times 10^6 \, {J}\)

Hint:

Always check the units and make sure the calculation matches the expected physical context. The internal energy calculation typically requires the specific heat at constant volume and the temperature change if the process is not isothermal.

Answer 1

The Correct Option is C

The problem does not specify the type of process the gas undergoes or the temperature, which typically are required to calculate internal energy or other forms of energy associated with the state of the gas. To find the internal energy (\(U\)) for an ideal gas without temperature information, we can estimate it under the assumption of an isothermal process using the ideal gas law: \[ PV = nRT \] However, without the temperature (\(T\)), number of moles (\(n\)), or the specific gas constant (\(R\)), we cannot directly calculate \(U\). For a monoatomic ideal gas, the internal energy can be expressed as: \[ U = \frac{3}{2} PV \] Using the given values: \[ U = \frac{3}{2} \times 3 \times 10^5 \, {Pa} \times 3 \, {m}^3 = 1.35 \times 10^6 \, {J} \] This value doesn't directly match any of the options, suggesting a possible misprint in the question or answers. Assuming \(13.5 \times 10^5 \, {J}\) was intended to be correct, it could be an error in the values presented in the options.