Answer: Mass of the planet, M= 8.53 x 10^8kg
Explanation:
Given Radius = 2.0 x 106m
Period T = 7h 11m
Using the third law of kepler's equation which states that the square of the orbital period of any planet is proportional to the cube of the semi-major axis of its orbit.
This is represented by the equation
T^2 = ( 4π^2/GM) R^3
Where T is the period in seconds
T = (7h x 60m + 11m)(60 sec)
= 25860 sec
G represents the gravitational constant
= 6.6 x 10^-11 N.m^2/kg^2 and M is the mass of the planet
Making M the subject of the formula,
M = (4π^2/G)*R^3/T^2
M = (4π^2/ 6.6 x10^-11)*(2×106m)^3(25860s)^2
Therefore Mass of the planet, M= 8.53 x 10^8kg
Efficiency η of a Carnot engine is defined to be:
<span>η = 1 - Tc / Th = (Th - Tc) / Th </span>
<span>where </span>
<span>Tc is the absolute temperature of the cold reservoir, and </span>
<span>Th is the absolute temperature of the hot reservoir. </span>
<span>In this case, given is η=22% and Th - Tc = 75K </span>
<span>Notice that although temperature difference is given in °C it has same numerical value in Kelvins because magnitude of the degree Celsius is exactly equal to that of the Kelvin (the difference between two scales is only in their starting points). </span>
<span>Th = (Th - Tc) / η </span>
<span>Th = 75 / 0.22 = 341 K (rounded to closest number) </span>
<span>Tc = Th - 75 = 266 K </span>
<span>Lower temperature is Tc = 266 K </span>
<span>Higher temperature is Th = 341 K</span>
The prime factors that affect the ability of substances to transfer the thermal energy to heat are the temperature difference between the two objects, area of cross-section, time, and distance travelled by the thermal energy.
<u>Explanation:
</u>
The process of heat conduction takes place through contact between two or more objects. But this conduction depends on multiple factors that are responsible for thermal conduction. They are-
- Temperature Difference(
) - The two objects must have a temperature difference else there will be no thermal conduction between them. The more the difference in their temperatures, the more thermal energy flows from one object to the other.
- Area of Cross-section (A) - Larger areas of contact provide as better medium of thermal conduction.
- Time (t) - The more time we give for the thermal conduction, the more energy is transmitted from one system to the other.
- Distance Travelled (l) - The longer the distance, lesser the conduction. Means, the distance should be minimized in order to achieve the optimum thermal conduction between two objects.
Consider metal pot and its handle, it is being boiled for 15 m. The molecules present near the source of heat, showing fast vibration and bounce off. It actually indicates the heats of substance. That’s why, handle remains hot as heat conduction takes place. It can be estimated by,

k - Thermal conductivity of the material, measured in J/s.m.