MHTCET 25 Apr 2025 Shift 2 Paper

Concept:The combined gas law is used for a fixed amount of gas when pressure, volume, and temperature all change.Explanation:First, convert the given temperatures from Celsius to Kelvin.$T_1 = 27 + 273 = 300 \,K$$T_2 = -3 + 273 = 270 \,K$The initial conditions are $P_1 = 1 \,atm$ and $V_1 = 500 \,m^3$.The final pressure is given as $P_2 = 0.5 \,atm$.Since the mass of helium gas is constant, the combined gas law applies.The formula is:$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$Substitute the known values into the equation.$$\frac{1 \times 500}{300} = \frac{0.5 \times V_2}{270}$$Rearrange the equation to solve for $V_2$.$$V_2 = \frac{500 \times 270}{300 \times 0.5}$$Simplify the numerator and denominator.$$V_2 = \frac{135000}{150} = 900 \,m^3$$Answer:The final volume of helium gas is $900 \,m^3$, which matches option C.