- #1
patric44
- 296
- 39
- Homework Statement
- a gas was at a specific vessel at T=300K, P=110KPa, when moved to another different vessel at the same temperature its pressure becomes 105KPa, if this vessel was heated to 330K find the percentage change in the density?
- Relevant Equations
- P1V1=P2V2, V1/T1=V2/T2
Hi all, in this question i was asked to find the percentage change in the density, my approach was as following, first i find the change in volume due to putting the gas into the other vessel as:
$$
P_{1}V_{1}=P_{2}V_{2}\;\; → \;\;V_{2}=\frac{P_{1}}{P_{2}}V_{1}
$$
now i use
$$
V_{1}/T_{1}=V_{2}/T_{2}\;\; → \;\;\frac{P_{1}}{P_{2}}V_{1}/T_{1}=V_{2}/T_{2}
$$
and using V=m/rho leads to, with m constant, i arrive at
$$
\frac{\rho_{o}-\rho_{2}}{\rho_{o}}=\frac{1}{\frac{T_{2}P_{1}}{T_{1}P_{2}}}-1=-13.22%
$$
the answer has the choices [-5.55% , -4.55% , 4%, 5%]
what I am doing wrong, can any one help
$$
P_{1}V_{1}=P_{2}V_{2}\;\; → \;\;V_{2}=\frac{P_{1}}{P_{2}}V_{1}
$$
now i use
$$
V_{1}/T_{1}=V_{2}/T_{2}\;\; → \;\;\frac{P_{1}}{P_{2}}V_{1}/T_{1}=V_{2}/T_{2}
$$
and using V=m/rho leads to, with m constant, i arrive at
$$
\frac{\rho_{o}-\rho_{2}}{\rho_{o}}=\frac{1}{\frac{T_{2}P_{1}}{T_{1}P_{2}}}-1=-13.22%
$$
the answer has the choices [-5.55% , -4.55% , 4%, 5%]
what I am doing wrong, can any one help
, so the change in density only comes from the movment in the other vessel which I can determine by Boyle's law, thanks so much its clear now