A vessel of volume `V_(0)` contains an ideal gas at pressure `p_(0)`and temperature T. Gas is continuously pumped out of this vessel at a constant volume-rate `dV/dt=r` keeping the temperature constant, The pressure inside the vessel. Find (a) the pressure of the gas as a function of time,(b) the time taken before half the original gas is pumped out.

Explanation

To solve the problem step by step, we will break it down into two parts as requested:

### Part (a): Finding the Pressure of the Gas as a Function of Time

1. **Understanding the Initial Conditions**:
- We start with a vessel of volume \( V_0 \) containing an ideal gas at pressure \( P_0 \) and temperature \( T \).
- The gas is being pumped out at a constant volume rate \( \frac{dV}{dt} = -r \) (negative because the volume of gas in the vessel is decreasing).

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