A person measure the presssures of his car tyre to be `2 times 10^5 Pa` At that time the temperature and pressure of the atmosphere are `27^@C`and `1 times 10^5 Pa` respectively. Then he travels to another city where the temperature and pressure of the atmosphere are `12^@C` and `6.7 times 10^4 Pa` respectively. Them what will be the pressure of his car tyre at that time. Assume the volume of the tyre is same in both cases.

Explanation

The pressure in a tyre is a guage pressure which is the difference between the pressure in the tyre and atmospheric pressure.
Hence, absolute pressure in the tyre=guage pressure + atmospheric pressure.
So in 1st case
absolte pressure, `p_1=2 times 10^5+10^5=3 times 10^5 Pa`
and temperature `T_1=273+27=300 K`
Let the 2nd case the measured pressure (gauge pressure) =x Pa.
So the absolute pressure `p_2=(x+6.7 times 10^4)Pa`
and temperature ,`T_2=273+12=285K`
Since the volume of the tyre is constant , `p_1/T_1=p_2/T_2`
or, `(3times 10^5)/300=(x+6.7times10^4)/285or,x=2.18 times 10^5`
So the measured pressure is `2.18 times 10^5 Pa`.