An ideal gas has a molar heat capacity at constant pressure of `Cp = 2.5 R`. The gas is kept in a closed vessel of volume `0.0083 m^(3)`, at a temperature of `300 K` and a pressure of 1.6 x 10^(6) Nm^(-2). An amount 2.49 x 10^(4) J of heat energy is supplied to the gas. calculate the final temperature and pressure of the gas.

Explanation

To solve the problem step by step, we will follow the principles of thermodynamics and the ideal gas law.

### Step 1: Identify the given values
- Molar heat capacity at constant pressure, \( C_p = 2.5 R \)
- Initial temperature, \( T_i = 300 \, K \)
- Initial pressure, \( P_i = 1.6 \times 10^6 \, N/m^2 \)
- Volume, \( V = 0.0083 \, m^3 \)
- Heat added, \( \Delta Q = 2.49 \times 10^4 \, J \)
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