Saved Bookmarks
| 1. |
An ideal gas has a specific heat at constant pressure C_P=(5 R/2). The gas is kept in a closed vessel of volume 0.0083 m^3, at a temperature of 300 K and a pressure of 1.6 xx10^6 N//m^2. An amount of 2.49xx10^4 Jof heat energy is supplied to the gas. Calculate the final temperature and pressure of the gas. |
|
Answer» Solution :Given that initial pressure, volume and temperature of gas is `P_1=1.6xx10^6 N//m^2` `V_1=0.0083m^3` `T_1`=300 K From gas law we can FIND the number of moles of gas in the CONTAINER as `n=(PV)/(RT)=(1.6xx10^6xx0.0083)/(8.314xx300)` `=16/3`mole It is given thatmolar specificheat of gas at constantpressureis `C_P=(5R)/2` THUS gas is monoatomic, hence its MOLAR specific heat at constant volume is given as `C_V=(3R)/2` As gas is heated in a closed vessel i.e. at constant volume, if its temperature is raised from `T_1` to `T_2` then, we have heat supplied to the gas is `Q=n C_V(T_2-T_1)` or `2.49xx10^4=16/3xx3/2R(T_2-300)` or `T_2=300+(3xx2xx2.49xx10^4)/(16xx3xx8.314)` `=300+374.36` =674.36 K For constantvolume process ,we have `P_2/P_1=T_2/T_1` Thus `P_2=T_2/T_1xxP_1` `=674.36/300xx1.6xx10^6` `=3.6xx10^6 N//m^2` |
|