If an ideal gas with internal energy U at 200°C is heated to 400°C, what happens to its internal energy?

The internal energy of an ideal gas is primarily a function of its temperature. For an ideal gas, the internal energy is proportional to the temperature measured in an absolute scale, such as Kelvin.

When the gas is heated from 200°C to 400°C, we first convert these temperatures to Kelvin. The temperature in Kelvin is calculated by adding 273.15 to the Celsius temperature. So:

• 200°C = 200 + 273.15 = 473.15 K

• 400°C = 400 + 273.15 = 673.15 K

The change in internal energy for an ideal gas can be approximated using the formula ΔU = nC_vΔT, where n is the number of moles, C_v is the specific heat at constant volume, and ΔT is the change in temperature in Kelvin.

Calculating the temperature difference:

ΔT = 673.15 K - 473.15 K = 200 K

Since internal energy depends on temperature, and we see that the temperature increases by a factor of approximately 1.4 when moving from 473.15 K to 673.15 K.

Thus, as the temperature increases, the internal energy increases also,