We can use the ideal gas law to solve for the temperature:
PV = nRT
where:
P = pressure = 5.213 atm
V = volume = 36.81 L
n = moles = 2.845 mol
R = gas constant = 0.08206 L·atm/mol·K
Solving for T:
T = PV/nR
T = (5.213 atm * 36.81 L) / (2.845 mol * 0.08206 L·atm/mol·K)
T = 548.8 K
Converting from Kelvin to Celsius:
T = 548.8 K - 273.15
T = 275.65°C
Therefore, the temperature inside the balloon is approximately 275.65°C, which is closest to option (d) 278.1°C.