Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. the temperature of the gaseous planet varies linearly with the height of the atmosphere. the delicate instruments on board completely fail at a height of 61.5 kilometers. what is the approximate temperature at this altitude? a. 200 k b. 250 k c. 300 k d. 400 k e. 450 k

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.

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explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."