the temperature of monoatomic gas was increased from t1=27c to t2=177c. by how many times the internal energy of the gas increase?

The internal energy increases 1.5 times

Explanation:

the internal energy of a mono atomic gas is given by E = 3/2kT

T1 = 27⁰C = 27+273=300 K

T2=177⁰C = 177+273=450 K

E1 = 3/2 k (300)

E2=3/2 k (450)

so E2/E1=[3/2 k (450) ][3/2 k (300) ]

E2/E1=450/300

E2 = 1.5 E1

so the internal energy increases by a factor of 1.5