C19 P61
a) 
1.8 * 176^y = 5.51 * 79.2^y
2.2222^y = 3.061111
y = ln(3.061111) / ln(2.222222) = 1.4
=> diatomic gas
b) 
so,
310 * 176^1.4 = T * 79.2^1.4
T = 948.1K
c) PV = nRT
so n = PV/RT
p = 1.80atm, 1 atm = 101325 Pa
V = 176L = 176000cm3 = 0.176 m3
R = 8.314 J·K−1mol-1
T = 310K
thus, n = 6.92 mol
Part b careless.... Equation is still correct... Anyway you
should also help check for careless mistake mah... Not just take
the values and use them without trying to understand how the
equation was used...
The power should be 0.4, not 1.4
310 * 176^0.4 = T * 79.2^0.4
T = 426.65K
Part c is already ideal gas equation. Maybe you could help check
if the calculations are wrong...