Answer:
The increase in the internal energy of the system is 360 Joules.
Explanation:
Given that,
Heat supplied to a system, Q = 292 J
Work done on the system by its surroundings, W = 68 J
We need to find the increase in the internal energy of the system. It can be given by first law of thermodynamics. It is given by :

So, the increase in the internal energy of the system is 360 Joules. Hence, this is the required solution.
Answer
Applying Wein's displacement

1) for sun T = 5800 K


2) for tungsten T = 2500 K


3) for heated metal T = 1500 K


4) for human skin T = 305 K


5) for cryogenically cooled metal T = 60 K


range of different spectrum
UV ----0.01-0.4
visible----0.4-0.7
infrared------0.7-100
for sun T = 5800
λ 0.01 0.4 0.7 100
λT 58 2320 4060 5.8 x 10⁵
F 0 0.125 0.491 1
fractions
for UV = 0.125
for visible = 0.441-0.125 = 0.366
for infrared = 1 -0.491 = 0.509