Final answer:
To find the new temperature of an ideal gas when its thermal energy is reduced by 10%, we calculate a 10% reduction in absolute temperature (Kelvin) from the initial temperature, then convert it back to Celsius. In this case, the new temperature would be -9.3 °C.
Step-by-step explanation:
To calculate the new temperature of an ideal gas after reducing its thermal energy by 10%, we first need to understand that the thermal energy of an ideal gas is directly proportional to its absolute temperature. Thus, a 10% reduction in thermal energy will also mean a 10% reduction in the absolute temperature. Given the initial temperature is 20 °C, we convert that to kelvins (293 K), calculate 10% of it, and then subtract that from the original temperature to find the new temperature in kelvins. Lastly, we'll convert the new temperature back to °C.
First, convert the initial temperature from Celsius to Kelvin:
20 °C + 273 = 293 K.
Calculate 10% of the initial temperature in Kelvin:
10% of 293 K = 29.3 K.
Subtract the 10% from the original temperature:
293 K - 29.3 K = 263.7 K.
Finally, convert the new temperature back to Celsius:
263.7 K - 273 = -9.3 °C.
Therefore, the new temperature of the ideal gas is -9.3 °C after a 10% reduction in its thermal energy.