1.you have an unknown amount of water vapor floating in a sealed container at 126℃. after 30 min the container is cooled to -26℃, and a solid sample of water is found at 2.5g. what amount of energy was used for this process to occur?

7.8 kJ. The process used 7.8 kJ.

The container is sealed, so

mass of water vapour = mass of water = mass of ice.

∴ Heat required = heat to cool vapour + heat to condense vapour to water + heat to cool water + heat to freeze water + heat to cool ice

q = q_1 + q_2 + q_3 + q_4 + q_5

Step 1. Calculate q_1

q_1 = mC_1ΔT_1

m = 2.5 g; C_1 = 1.996 J.°C^(-1)g^(-1)

ΔT_1 = T_f – T_i  = 100 °C – 126 °C = -26 °C

q_1 = 2.5 g × 1.996 J.°C^(-1)g^(-1) × (-26°C) = -130 J

The negative sign shows that heat is removed from the system.

Step 2. Calculate q_2

q_2 = mΔ_cH

Δ_cH = -2257 J·g^(-1)

q_2 = 2.5 g × [-2257 J·g^(-1)] = -5640 J

Step 3. Calculate q_3

q_3 = mC_3ΔT_3

C_3 = 4.182 J.°C^(-1)g^(-1); ΔT_3 = T_f – T_i  = 0 °C – 100 °C = -100 °C

q_3 = 2.5 g × 4.182 J.°C^(-1)g^(-1) × (-100 °C) = -1050 J

Step 4. Calculate q_4

q_4 = mΔ_cH

Δ_cH = -334 J·g^(-1)

q_4 = 2.5 g × [-334 J·g^(-1)] = -835 J

Step 5. Calculate q_5

q_5 = mC_5ΔT_5

C_5 = 2.090 J.°C^(-1)g^(-1); ΔT_3 = T_f – T_i  = -26 °C –0 °C = -26 °C

q_5 = 2.5 g × 2.090 J.°C^(-1)g^(-1) × (-26 °C) = -136 J

Step 6. Calculate the total heat involved

q = q_1 + q_2 + q_3 + q_4 + q_5

= (-130 – 5640 – 1050 – 835 – 136) J = -7800 J = -7.8 kJ

The process removed 7.8 kJ.

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).