Question

5gm of unknown gas has pressure P at a temperature T K in a vessel. On increasing the temperature by \[{50^ \circ }C\], 1gm of the gas was taken out to maintain the pressure P. The original temperature T was:
(A) 73K
(B) 100K
(C) 200K
(D) None of these

Answer 1

Hint: We can use the ideal gas equation PV=nRT in initial and final state to solve this problem. Formula for number of moles is \[n = \frac{{{\text{weight of gas}}}}{{{\text{molecular weight of gas}}}}\]


Complete step by step solution:
Here we are given to find the temperature and amount of gas taken out and the relative pressure is given. We can simply use the ideal gas equation for both the cases and find out the temperature.

We know that PV=nRT where n=moles of gas.......(1)
For the initial condition, we can assume that Pressure is P, Volume is V, and temperature is T but we can’t put the weight of the gas in this equation, so we will have to use the formula of moles to get a clear idea.
Here number of moles, \[n = \frac{{{\text{weight of gas}}}}{{{\text{molecular weight of gas}}}}\]= \[\frac{W}{{MW}}\]...........(2)
Let’s put equation (2) into equation (1)
\[PV = \frac{{WRT}}{{M.W.}}\] .........(3)
Now, values of P, R, V and M.W. will remain constant in both the states, so we can write this equation as \[\frac{{PV \times M.W.}}{R} = W \times T\]..........(4)
Now put values of both initial and final state into equation (4),
For initial state, we will get \[\frac{{PV \times M.W.}}{R} = 5 \times T\]..............(5)
For final state, we will get \[\frac{{PV \times M.W.}}{R} = 4 \times (T + 50)\]..............(6)
Now left hand side of equation (5) and (6) are same, so we can write that
\[5 \times T = 4 \times (T + 50)\]
Now we will find the value of T by mathematical steps.
\[5T = 4T + 200\]
Therefore, T=200K
So, we can say that the temperature T they asked to find is 200K.

Therefore the correct answer is (C) 200K


Note: Remember that the temperature we obtain or put in the ideal gas equation is always in Kelvin and if we put it in Celsius, then it will not give the correct answer. Remember that in these types of questions where two states are there-final and initial, then we have to make two equations and then comparing them will give us the answer, just putting the values of the final state will not take us to the answer.