1. The solar energy received by earth is only a small portion of radiation energy released by the sun due to its high temperature. Please find the solar energy received by the earth each day. You can find the parameters needed (such as diameter of sun and earth, distance between them, and temperature of sun, etc) on‐line and made reasonable assumptions as needed. The calculation method of the area of spherical cap can be found in website:‐cap‐volume‐surface‐area‐calculator.html

2. Figure shows a small tea kettle designed to heat 1 kg water to boiling using a 1000 W resister heater.
You can assume the heat (thermal energy) is lost through the surface except bottom. The convection heat loss coefficient is 40 W/m². When designed, you need consider 10% extra volume so that the boiling water will not spill out.
(a) Please describe the thermodynamic process and heat transfer mode involved in this question;  
(b) Please list the assumptions in solving this question.  
(c) Find the most energy efficient design (radius of the bottom) using the boiling point of water as reference. You can make assumptions as needed but must be reasonable. Please list your assumptions.   
(d) Please justify if you can ignore the radiation heat loss when water temperature reaches 50 and 100 °C, respectively. You can use the design derived in (c);
(d) Find the function describing the changes of water temperature with time. You can assume the initial temperature of water and kettle is 20 °C and ignore the heat needed in heating the stainless steel kettle itself. You can use the design derived in (c).

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