Problem 5.15 The temperature in a certain region of space is given by T = To - A(2x² + y? + 2?) (in kelvin). Distances are in meters and the constant 4 has the value 0.5 kelvin/m². The value of To is 300 K. (a) At point (1,2,2) what is the direction and rate (in K/m) of marimum temperature increase? (b) If you move one meter in that direction what is the temperature at the new position? (c) The temperature at the new position as calculated by the formula is not equal to the value odtained by multiplying the rate of temperature decrease by the displacement. Explain this discrepancy.

The Statue of Liberty in New York City is approximately 305 ft305 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm1.35 mm thick. number of dimes:     Each dime has a mass of 2.268 g.2.268 g. How much would the stack of dimes from the previous question weigh? mass:   g What is the value, in dollars, of the same stack of dimes? value:   dollars The 2017 U.S. gross domestic product (GDP) was valued at 19,390,604,000 dollars.19,390,604,000 dollars. How many Statue of Liberty‑height stacks of dimes are needed to match the GDP in value? number of stacks:

1. a. Derive the following expression for the fractional change in the speed of sound (dv/v) dv 1 dT related to a small change in temperature (dT): Start with the expression for the 2 T YRT M speed of sound related to temperature: v= where y is the ratio of heat capacities (a constant), R is the gas constant and M is the molar mass of the substance. Show enough steps (and words!) so that I can tell what you're doing. b. Use the red equation above to determine what the speed of sound in air at 21.0° C is, given that the speed of sound at 20.0° C is 344 m/s. Check your answer against any reference that has the speed of sound in air at different temperatures. Show your setup, and remember that the speed should not be terribly different! Hint: What temperature units should you be using?

The number density of gas atoms at a certain location in the space above our planet is about 0.75 × 10!1 m²³, and the pressure is 2.9 x 10- 10 Pa in this region. What is the temperature in this region, in degrees Celsius? T =

A hot tub with a surface area of 28 ft2 is filled with water to a depth of 29 in . Hint: volume is calculated as area × height (A × h). A) What is the volume of water in the tub, in liters? Express your answer to two significant figures and include the appropriate units. B) How many kilojoules are needed to heat the water from 59∘F to 103 ∘F? Express your answer to two significant figures and include the appropriate units. C) If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 59∘F to 103∘F? Express your answer to two significant figures and include the appropriate units.

The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawis so that its position after t seconds is given by where x and y are measured in centimeters. The temperature function satisfles T3, 6) 2 and T(3, 6) -7. How fast is the temperature rising on the bug's path after 2 seconds? (Round your answer to two decimal places.) C/s Need Help? Read Watch Master t

When the coefficient of linear expansion, a, and the temperature change, T-T, are large, a length L, of a solid substance expands in length to a(T, -T₂) L₁ = L₁e O L=L[1 + a(Tƒ– T;)]. ○ Ly=al (Ty-T). O L=L[1 + In(a(T₁-T))]. a(T, I₂ = ₁₂₁[ 1 + ª²(²₁-7)].