Question

Воздушный шар объёмом 400м куб наполнили гелием при давлении 100000м куб. Солнце нагревает газ на 8К Какова начальная температура газа, если его внутренняя энергия увеличилась на 1600000Дж?

Answer 1

100000/400=250
250*8=2000
1600000/2000=800

Answer 2

Calculation of Initial Temperature of Gas in a Hot Air Balloon

To calculate the initial temperature of the gas in the hot air balloon, we can use the equation for the change in internal energy of an ideal gas:

ΔU = nCvΔT

Where: - ΔU is the change in internal energy of the gas - n is the number of moles of gas - Cv is the molar specific heat capacity at constant volume - ΔT is the change in temperature

In this case, the gas in the hot air balloon is helium, which is a monoatomic gas. The molar specific heat capacity at constant volume for monoatomic gases is approximately 3/2R, where R is the ideal gas constant.

Given: - Volume of the balloon (V) = 400 m^3 - Pressure of the gas (P) = 100,000 m^3 - Change in temperature (ΔT) = 8 K - Change in internal energy (ΔU) = 1,600,000 J

To find the initial temperature (T1), we need to calculate the number of moles of helium gas (n) using the ideal gas law:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of gas - R is the ideal gas constant - T is the temperature of the gas

Rearranging the equation, we have:

n = PV / RT

Substituting the given values, we can calculate the number of moles of helium gas:

n = (100,000 m^3) / (8.314 J/(mol·K) * T1)

Now, we can substitute the values of n and Cv into the equation for the change in internal energy:

ΔU = n * Cv * ΔT

Substituting the given values, we can solve for the initial temperature (T1):

1,600,000 J = (100,000 m^3) / (8.314 J/(mol·K) * T1) * (3/2 * 8.314 J/(mol·K)) * 8 K

Simplifying the equation, we get:

1,600,000 J = (100,000 m^3) / T1 * 3/2 * 8.314 J/(mol·K) * 8 K

Now, we can solve for T1:

T1 = (100,000 m^3) / (1,600,000 J / (3/2 * 8.314 J/(mol·K) * 8 K))

Calculating the value, we find:

T1 ≈ 7,228 K

Therefore, the initial temperature of the gas in the hot air balloon is approximately 7,228 K.

[[1]]