Answer: E. 450 K
Explanation:
It is given that the temperature of the gaseous planet is linearly related with height of the atmosphere. we can write this in the mathematical equation:
y = m x +c
where y is the temperature values, x is height, m is the slope and c is the y-intercept. we have been given two sets of value in the image, using which we can find the value of slope in y-intercept.
at x = 18.40 km, y = 147.54 K
⇒147.54 = 18.40 m + c
⇒c = 147.54 - 18.40 m ..(1)
at x =78.11 km, y = 567.00 K
⇒567.00 =78.11 m + c ..(2)
Put equation 1 in 2 and solve:
⇒567.00 =78.11 m + 147.54 - 18.40 m
⇒419.46 = 59.71 m
⇒ m =419.46 ÷59.71 = 7.025 K/km
c = 147.54 - 18.40 × 7.025 = 18.28 K
At height, x = 61.5 km the approximate temperature is :
y = 7.025 K/km × 61.5 km + 18.28 K = 450.3 K
Thus, the approximate temperature at altitude 61.5 km is 450 K.
