At `27^(@)C` a motor car tyre has pressure of 2 atmosphere. Find the temperautre. If the tyre suddenly bursts. (Given, `gamma_("air")=1.4`)

Options

A. 246.1 K
B. 250 K
C. 290 K
D. 248 K

Answer

A

Explanation

When a system undergoes a change under conition, that no exchange of heat takes place between the system and surroundings , then such a process is called adiabatic.
`p^((1-gamma))T^(gamma)`
`gamma` is ratio of specific heats , p is pressure and T is temperature.
`therefore" "((p_(2))/(p_(1)))^((gamma-1))=((T_(2))/(T_(1)))^(gamma)rArr((1)/(2))^(0.4)=((T_(2))/(300))^(1.4)`
`therefore" " 0.4["log"1-"log"2]=1.4["log"T_(2)-"log"300]`
`0.4"log"((1)/(2))=1.4"log"g((T_(2))/(300))((1)/(2))^(2//7)=(T_(2))/(300)`
`rArr" " T_(2)=246.1K`