QUESTION FOUR (20 MARKS) a) State: i) The first law of thermodynamics in terms of internal energy and state the significance of the law. (3 marks) ii) A gas is compressed at a constant pressure of 0.5 atm from 5.0 litres to 2.0 lit- res, losing 500 J of heat in the process Find the change in internal energy. (5 marks) b) A 200 g ice initially at -20^circ C is heated to become water vapour at 100^circ C. What amount of heat energy is used in this process? (7marks) c) The sun radiates energy at the rate of 6.5times 10^7W/m^2 from its surface. Assuming that the sun radiates as a blackbody (which is approximately true), find its surface temperature? The emissivity of a blackbody is e=1. (5 marks)

a) i) Theodynamics states that be expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. The significance of this law is that it provides a relationship between heat, work, and internal energy, which is fundamental in understanding the energy changes in thermodynamic systems.<br /><br />ii) To find the change in internal energy, we can use the first law of thermodynamics. Given that the gas is compressed at constant pressure, the work done by the gas is given by W = PΔV, where P is the pressure and ΔV is the change in volume. The heat lost by the gas is given as -500 J (negative because heat is lost). Substituting the values, we get ΔU = - (0.5 J + 1.5 atm·L = -500 J + 150 J = -350 J. Therefore, the change in internal energy is -350 J.<br /><br />b) To find the amount of heat energy used in this process, we need to consider the different stages of the process. First, the ice is heated from -20°C to 0°C, then it melts to become water, and finally, the water is heated from 0°C to 100°C. The heat energy required for each stage can be calculated using the specific heat capacities and the mass of the ice. The total heat energy used is the sum of the heat energy required for each stage.<br /><br />c) The sun radiates energy as a blackbody, and we can use the Stefan-Boltzmann law to find its surface temperature. The Stefan-Boltzmann law states that the total energy per unit surface area of a black radiated per unit surface area, σ is the Stefan-Boltzmann constant, and T is the absolute temperature. Rearranging the equation, we get T = (E/σ)^(1/4). Substituting the given value of E and the value of σ (5.67 × 10^-8 W/m^2·K^4), we can calculate the surface temperature of the sun.