The temperature, pressure and volume of two gases X and Y are T, P and V respectively. When the gases are mixed then the volume and temperature of mixture become V and T respectively. The pressure and mass of the mixture will be

The correct option is 2P and 2M.

Let's determine the mass and the pressure of the mixture step-by-step.

1. Mass of the mixture:
According to the law of conservation of mass, mass is an additive property. If gas X has a mass of M and gas Y has a mass of M, then the total mass of the mixture is simply the sum of their individual masses:

$M_{\text{mixture}}=M_X+M_Y=M+M=2M$

2. Pressure of the mixture:
We can find the final pressure of the mixture by using the ideal gas equation:

$PV=nRT$

where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature.

For gas X, the pressure is P, the volume is V, and the temperature is T. The number of moles of gas X is:

$n_X=\frac{PV}{RT}$

For gas Y, the pressure is also P, the volume is V, and the temperature is T. The number of moles of gas Y is:

$n_Y=\frac{PV}{RT}$

When the two gases are mixed, the total number of moles in the mixture is the sum of the moles of the individual gases:

$n_{\text{total}}=n_X+n_Y=\frac{PV}{RT}+\frac{PV}{RT}=\frac{2PV}{RT}$

Let the pressure of the mixture be P'. The volume of the mixture is V, and its temperature is T. Applying the ideal gas equation to the mixture:

$P^{\prime }V=n_{\text{total}}RT$

Substituting the expression for the total number of moles:

$P^{\prime }V=\left(\frac{2PV}{RT}\right)RT$

Simplifying the right side of the equation:

$P^{\prime }V=2PV$

Dividing both sides by the volume V, we find:

$P^{\prime }=2P$

Thus, the pressure of the mixture will be 2P and the mass of the mixture will be 2M.