Question

The temperature of 2 kg of neon is increased from 20 to \(180^{\circ} \mathrm{C}\). Calculate the change in the total internal energy of the neon, in \(\mathrm{kJ}\). Would the internal energy change be any different if the neon were replaced with argon?

Short answer

Would the internal energy change be different if neon were replaced with argon?

Step-by-step solution

Convert temperature to Kelvin.

First, we need to convert the given temperatures from Celsius to Kelvin, as the calculations should be performed in Kelvin. K = °C + 273.15 Initial temperature (T1): 20°C = 293.15 K Final temperature (T2): 180°C = 453.15 K

Calculate the change in temperature (ΔT)

Now, we will calculate the change in temperature. ΔT = T2 - T1 = 453.15 K - 293.15 K = 160 K

Find the specific heat capacity and mass

We are given that the mass (m) of the neon is 2 kg. The specific heat capacity (c) of neon is 1.03 J/g*K (joules per gram per Kelvin). Since we have the mass in kilograms, we will convert the specific heat capacity to J/kg*K (joules per kilogram per Kelvin). 1 kg = 1000 g c = 1.03 J/g*K × 1000 g/kg = 1030 J/kg*K

Calculate the change in internal energy (ΔU) for neon

Now, we will use the formula: ΔU = mcΔT ΔU = (2 kg) × (1030 J/kg*K) × (160 K) ΔU = 328960 J Since we need the answer in kJ, we will convert from J to kJ. 1 kJ = 1000 J ΔU = 328960 J ÷ 1000 = 328.96 kJ The change in total internal energy of the neon is 328.96 kJ.

Evaluate the internal energy change for argon

To find out if the internal energy change would be different for argon, we need to know the specific heat capacity of argon. The specific heat capacity of argon is 0.520 J/g*K, which is different from neon's specific heat capacity. This means that the internal energy change for argon would also be different. In conclusion, the change in the total internal energy of 2 kg of neon when its temperature is increased from 293.15 K to 453.15 K is 328.96 kJ. If neon were replaced with argon, the internal energy change would be different.