MATHPHYS HELP
PLS PHYSICS IS MUCH HARDER NOT BEING IN SCHOOL

(001) 4. Heating 100 g of water from 10°C to 50°C

(002) 4.32 km

(003) 5. B only

(004) 347°C

(005) 73.5 °C

(006) 4.9 g

(007) 3. Adding the same amount of heat to two different objects will produce the same increase in temperature.

Explanation:

(001) Heat is the product of mass, specific heat capacity, and temperature change.

q = mCΔT

The specific heat of water is 1 cal/g/°C.  So the heat required for each is:

1. q = (1000 g) (1 cal/g/°C) (12°C − 10°C) = 2000 cal

2. q = (10 g) (1 cal/g/°C) (40°C − 10°C) = 300 cal

3. q = (1 g) (1 cal/g/°C) (80°C − 10°C) = 70 cal

4. q = (100 g) (1 cal/g/°C) (50°C − 10°C) = 4000 cal

(002) A "food Calorie" is 1 kcal = 1000 cal, or 4186 Joules.

Work = change in energy

W = ΔPE

W = mgΔh

758 kcal (4186 J/kcal) = (74.9 kg) (9.8 m/s²) h

h = 4320 m

h = 4.32 km

(003) Heat flows from higher temperature to lower temperature.

It's important to note that an object can have more thermal energy and still have a lower temperature.  For example, the ocean has low temperature but a very large mass, so it has more thermal energy than a cup of coffee, which has higher temperature but a much smaller mass.

(004) Kinetic energy = heat

KE = q

½ mv² = mCΔT

½ v² = CΔT

ΔT = v² / (2C)

ΔT = (298 m/s)² / (2 × 128 J/kg/°C)

ΔT = 347°C

(005) Heat gained by the glass = heat lost by water

m₁C₁ΔT₁ = -m₂C₂ΔT₂

(300 g) (0.2 cal/g/°C) (T − 32°C) = -(199 g) (1 cal/g/°C) (T − 86°C)

(60 cal/°C) (T − 32°C) = -(199 cal/°C) (T − 86°C)

(60 cal/°C) T − 1920 cal = -(199 cal/°C) T + 17114 cal

(259 cal/°C) T = 19034 cal

T = 73.5 °C

(006) Heat gained by ice = heat lost by water

m₁C₁ΔT₁ = m₂L₂

(49 g) (0.5 cal/g/°C) (0°C − (-16°C)) = m (80 cal/g)

392 cal = m (80 cal/g)

m = 4.9 g

(007) Heat is the product of mass, specific heat capacity, and temperature change.

q = mCΔT

So if two objects have different masses, or different heat capacities, then adding the same amount of heat will produce different increases in temperature.

Statement 3 is false.

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water